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<head>
    <meta charset="UTF-8">
    <title>Document</title>
    <meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=no, minimum-scale=1.0, maximum-scale=1.0">
    <script src="./jquery-1.11.0.js"></script>
</head>
<body>
    <div id="triggerInput">
        triggerInput
    </div>
    <input type="datetime-local" id="datePicker"/>

    <script>
        $(document).ready(function() {
            $('#triggerInput').click(function() {
                $('#datePicker').click();
                open($('#datePicker'));
            });
        });

        function open(elem) {
            if (document.createEvent) {
                var e = document.createEvent("MouseEvents");
                e.initMouseEvent("mousedown", true, true, window, 0, 0, 0, 0, 0, false, false, false, false, 0, null);
                elem[0].dispatchEvent(e);
            } else if (element.fireEvent) {
                elem[0].fireEvent("onmousedown");
            }
        }
    </script>
</body>
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